DETERMINATION OF THE NEUTRON MAGNETIC MOMENT

G.L. Greene and N.F. Ramsey

Harvard University, Cambridge, Massachusetts 02138

W. Mampe

Institut Laue-Langevin, 380A2 Grenoble, France -^...

J.M. Pendlebury and K. Smith \ '"-> -*,

University of Sussex, Falmer, Brighton, BNI 9 QH, United Kingdom

V!.B. Dress and P.D. Miller

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37838

Paul Perrin

Centre d'Etudes Nucleaires, 38042 Grenoble, France

The neutron magnetic inomenL has bae» measured with an improvement of a factor of 100 over the previous best neasurement. Using a magnetic resonance spectrometer of the separated oscillatory field type capable of determining a resonance signal for both neutrons and protons (in flowing 1^0), we find u /v = 0.68497935(17) (0.25 ppm). The neutron magnetic moment: can also be n p expressed without loss of accuracy in a variety of other units.

Key words: Flowing water NMR; magnetic resonance; neutron magnetic moment; particle properties.

Current address: Gibbs Laboratory, Physics Department, Yale University,

New Haven, Conn. 06520 ^^ ^ ^ .^^ ^

MASTER 1. Introduction

The realization that the neutron, a neutral particle, possesses a non-zero magnetic moment has been of considerable importance in the development of nuclear and particle physics. Even before any explicit measurement of p had been made, there was a strong indication that u f 0 from comparisons of the proton and deuteron magnetic moments u and p . If the neutron and proton combine in a pure S. state to form the deuteron, one would expect p_ = p + p . Early measurements of p and pD gave, according to this relation, p = -1.8 p., where p., is the nuclear magneton, n N N According to Dirac Theory, which assumes structureless, spin 1/2 particles, p =0 and p = p,,. The anomolous moments are defined as the n p h differences between the actual moments and the Dirac moments. The first serious attempt to explain the anomolous moments of the nucleons was made by

Frolich, Heitler and Kemmer [1] in 1938. Their "meson exchange theory" pre- dicted equal magnitudes and opposite signs for the anomolous proton and neutron moments [2], The actual magnitudes of the moments are much more difficult to obtain using this theory. Though subsequently refined by many others [3J the initial conclusions of Frolich, Heitler and Ketr.mer adequately summar- ized the state of the theoretical understanding of the neutron magnetic moment until the introduction of the quark, model.

The first explicit measurement of Lhe neutron magnetic moment was made by

Alverez and Bloch [4] in 19'iO. Using Rabi's magnetic resonance technique with a neutron beam obtained by deuteron bombardment of Be, they obtained a value of |u | = 1.93 ± 0.02 p . In general, no information about the sign of a magnetic moment is obtainable from a resonance experiment utilizing a purely oscillating magnetic field (In 1949 Rogers and Staub [5] determined the sign of p using a resonance technique that employed a rotating field. As had been thought, the sign was negative.)

2 The discovery by Kellog, Rabi, Ramsey and Zacharias [6] that the deuteron

has an electric quadropole moment implied that the ground state of the 3

deuteron could not, in fact, be accurately described by a pure S1 state but must have some admixture of D state. Thus the additivity of neutron and proton moments in the deuteron could not be exact. It was therefore of great interest to determine p more accurately so that it could be compared with the well known values of u and p_. P D

In 1947 Arnold and Roberts [7], using a neutron beam from a reactor,

determined p in a resonance experiment with a single oscillatory field.

They were able to obtain a more accurate value of |u | = 1.9103(12) u^ by

using the then novel technique of NMR as a means of field calibration. About

the same time, Bloch, Micodemus and Staub [81 also obtained a more accurate

value for p . They reported their result as the ratio of neutron to proton moment |p /p | = 0.685001(30).

With these more accurate values for u , it was possible to determine the

D.. admixture in the deuteron ground state by two independent means, through

the deuteron electric quadropole moment, or by comparison between u , u and

Pn- Gratifyingly, these independent values were consistant.

With the introduction of the quark model an appealing explanation for the value of the ratio of the neutron moment to the proton moment emerged.

Sakita [9] and Beg, Lee and Pais [10] pointed out that this ratio should be p /p = -2/3 [11] if the internal symmetry SU(3) is bioken only by electro- sagnetism. In this model, the ratios of ?11 the baryon ifioments are uniquely determined and easily calculated (Their absolute magnitudes are dependent on the quark magnetic moments. Determining these would require knowledge of the quark masses). The agreement between theory and experiment for u /u is considerably better than for other baryon pairs and is striking for such a simple theory. The approximately 3% discrepancy between theory and experiment should not be viewed as a significant disagreement. SU(3)® SU(2) (i.e 3 similar quarks with spin 1/2) is known to be an incomplete description for

strongly interacting particles.

At the initiation of the vork reported here, the uncertainty associated with theory far exceeded the experimental error of the best measurement of y [12]. As a result, theoretical considerations did not provide the dominant n motivation for the current work. Rather, the possibility of a substantial improvement in our knowledge of a fundamental particle property as well as the opportunity to demonstrate an elegant, new experimental technique prompted our effort.

The most accurate determination of u , prior to the work reported here, was that of Corngold, Cohen and Ramsey [12]. This experiment involved a thermal neutron beam and benefited from the use of the separated oscillatory field method. A result of |p /p | = 0.685039(17) was obtained. The major limitation to the accuracy of this measurement arose from the method used to calibrate the magnetic field. An NMR probe of small dimensions was employed to determine the field at a number of discrete locations. This field map was then used to give the appropriate field average by a pointwise integration.

The discrete nature of this stepwise integration led to the dominant error in the experimental result.

The current work benefit ted from several advances in experimental technique. Access to the high flux reactor of the Institut Laue-Langevin at

Grenoble, France, allowed the use of an intense "cold" neutron beam. Such

"cold" beams are characterized by low beam velocities. This led to an improvement of a factor of -5 over the line width obtained by Cohen, Corngold and Ramsey [12]. An additional advantage to the use of "cold" neutrons lies in the ability to employ neutron guides to reduce beam divergence and thei.^ ore increase the flux. Such guides also allowed a novel field calibration technique which provided the major improvement in experimental sensitivity. Following a suggestion of Purcell {13] made some time ago, the field was

monitored by obtaining a separated oscillatory field resonance signal with

water flowing through the neutron guide. In this fashion, the field average

taken by the protons in the water is the same as that taken by the neutrons.

Since all the relevant diamagnetic corrections for protons in water are known

to high accuracy, a direct measurement of the ratio of the neutron magnetic

moment to the proton magnetic moment was obtained. From this result, the

magnetic moment of the neutron can be expressed in a variety of other units.

2. Apparatus

The aim of the experimental technique was to measure the Larmor precession

frequency for neutrons and protons (in water) in precisely the same volume as

nearly simultaneously as possible. With the use of a neutron guide (a

glass tube of circular cross-section) it was a straight forward matter to

confine neutrons and water in the sair.e volume. One simply let the water flow

through the neutron guide. This procedure,however precluded the possibility of determining the resonance frequency for neutrons and protons with exact simultaneity. To insure that no spurious effects resulted from drifts during

the time required to make a change-over from neutron beam to flowing water, a second, parallel tube was installed in the spectrometer. Water was continuously sent through this tube to provide a field monitor. By alternating neutrons and protons in the principal tube t:hile protons flowed continuously in the monitor tube, errors due to field drifts could be detected and reduced to an insignificant level. This technique has been discussed in detail elsewhere

The cold source at the high flux reactor of the Institut Laue-Langevin

in Grenoble provided the source of neutrons used in this experiment. The

flux through the apparatus was typically 1.5 x 10 neutrons/s. The neutrons were polarized by glancing reflection from a magnetized mirror. A similar mirror was used to analyze the neutron polarization at the exit of the spec- trometer. The neutrons were detected by a Li loaded glass scintillator coupled to a photo-multiplier.

The protons in the flowing water were polarized by passage through a chamber placed in a high (~2kG) pre-polarizing magnet. As the protons spent more than one longitudinal relaxation time in this field, their polarization could be approximated by a simple Boltzman distribution. While the degree of polarization so obtained was very small, the enormous flux (by molecular beam standards) led to an easily detected signal. The proton polarization at exit was detected in a second high field region (-4kG) with slightly modified commercial NMR equipment.

The spectrometer was based on a high stability, high homogeneity, large volume electromagnet. The nominal field in the magnet was 18G. The separated oscillatory field coils (esch 3cm long) were mounted in the magnet with a separation of 61 cm. Surrounding each of the separated coils were independently controllable trim coils to adjust the fields at the coils.

The magnet and spectrometer were mounted in a two layer cylindrical

Molypermalloy magnetic shield to reduce the effects of time dependent external fields. The entire assembly was mounted on a large rotating platform. This allowed the orientation of the spectrometer with respect to beam velocity to be reversed.

All relevant electronics we^ interfaced (via CAMAC) to a PDP 11/10 computer. In this way all data collection and experimental control were carried out on line. 3. Results

Figures 1 and 2 show typical neutron and proton resonance lineshapes

obtained in this experiment. The dramatic difference in line widths

(~120Hz vs -0.8Hz) for neutrons and protons is due to the great difference in

particle velocities for the two cases. The neutron velocity was -150 m/sec

while the proton velocity was ~1 m/sec. The presence of many more side lobes

in the proton resonance is indicative of a narrower relative proton velocity

distribution.

The actual quantity measured in this experiment was the ratio between the

Larmor precession frequencies for neutrons in vacuum and for protons in a

cylindrical sample of water at 22°C. To arrive at this quantity, corrections

for several shifts and distortions had to be made.

The largest systematic effect resulted from the Bloch-Siegert effect [15].

This effect may be viewed as arising from the counter-rotating component

present in an oscillating field. It is a curious feature of the separated

oscillatory field technique that the shift resulting from this effect is not

strictly linear in oscillating field power t16]. However, this non-linearity

is well understood and can be simply accounted for. Figure 3 illustrates

the extrapolation technique which was used to account for the Bloch-Seigert

Shift.

The data shown in Figure 3 were taken in the two possible machine

orientations. These correspond to a reversal of the spectrometer with

respect to the beam velocity. The shift seen between the two orientations is

presumably due to geometrical imperfections in coil construction. It should be noted that the shifts seen in Figure 3 arise entirely from the distortion of the neutron resonance. The much lower velocity of the protons, and the consequent

reduction in oscillating power, implies negligible shifts in the proton

resonance frequency. Table 1 summarizes the significant shifts and errors in the measurement of the ratio of neutron moment to proton moment in a cylindrical sample of

H20 at 22°C , un/(o

un/w (cyl., H20, 22°) = 0.68499588(16) (0.24 ppm) (1)

The value of the magnetic moment of the neutron can be expressed in terms of the Bohr magneton UT> with little loss of accuracy through the relation a

Un u w (cyl, H-0, 22°) u (sph, H,0, 22°) p' X K } PB up (cyl, H20, 22°) Wp (sph, H20, 22°) u>p (sph, H^, 35°) ufi * where the notation "sph" refers to a spherical sample, and p' is the effective proton moment in a spherical sample of H-0 at 35°C as measured by Philips,

Cook and Kleppner [17].

The first ratio in the right hand side of Equation 2 is our experimental result. The second ratio is given by 1 - 2TTK/3 = 1 + 1-505(2) x 10~ from the data summarized by Tople e_t aj^ [18] where K is the volumetric suscep- tibility of water. The third ratio is taken to be 1 + 1-4 (1) x 10~ from the results of Hindman as interpreted in a footnote in Philips ££^1 [17].

The final ratio of p'/u_ is given by Philips et al [17]. From Equation 2 p B — —- we conclude

P , — = - 1-04187564 (26) x 10 J (0.25 ppm) (3) UB The slight increase in experimental error arises from the temperature correction in Equation 2.

Using the results of Winkler, Kleppner, Myint and Walther [19], we can express JJ in terms of the free electron moment y and free proton moment p by — = 1-04066884 (26) x 10 J (0.25 ppm) (4)

— - -0.68497935 (17) (0.25 ppm)

Our result can also be expressed in terms of the nuclear magneton u . In

this case, however, the accuracy is slightly degraded by the uncertainty in

the electron to proton mass ratio. Using the value of m/M obtained by

combining results from Philips ejt ad [17] and Cohen and Taylor 118] we have

— = - 1-91304184 (88) (0.45 ppm) (5)

4. Acknowledgements

We wish to express our thanks to the direction and staff of the Institut.

Laue Langevin for their assistance and hospitality during the course of this experiment. This work was supported in part by the Department of

Energy and the National Science Foundation (U.S.A.) and Le Department de

Recherche Fundamental du Commissariat a l'Energie Atomique (France). References and Footnotes

1. H. Frolich, W. Heitler and N. Kenuner, Proc. R. Soc. London 166, 154 (1938).

2. E. Fermi, in his book Nuclear Physics (University of Chicago Press, Chicago

1951) gives a simple explanation of the meson exchange model, though he

evidently did not think highly of the theory, calling it a "naive little

fantasy" (p. 13).

3. See G.L. Greene et_ al, Phys. Rev. D 20, 2139 (1979) for a more complete bibliography

4. L. Alverez and F. Bloch, Phys. Rev. 5_7, 111 (1940).

5. E.H. Roger, and H.R. Staub, Phys. Rev. _7Ji> 980 (1949).

6. J.M.B. Kellog, I.I. Rabi, N.F. Ramsey and J.R. Zacharias, Phys. Rev. 5_7,

677 (1940).

7. W. Arnold and A. Roberts, Phys. Rev. _7J., 878 (1947).

8. F. Bloch, D.B. Nicodemus and H.R. Staub, Phys. Rev. Th_, 1025 (1949).

9. B. Sakita, Phys. Rev. Lett. JL3 643 (1964).

10. M.A. Beg, B.W. Lee and A. Pais, Phys. Rev. Lett. 13, 514 (1964).

11. See also R.D. Young, Am. J. Phys. ^1 472 (1973) for a simple vector addition

argument which gives the -2/3 result. This argument was first suggested by

Beg et al.

12. V.W. Cohen, N.R. Corngold and N.F. Ramsey, Phys. Rev. 104, 283 (1956).

13. E.M. Purcell, Private Communication (1952).

14. G.L. Greene, Ph.D. Thesis, Harvard University (1977), available as Institut

Laue Langevin Technical Report 77GR2O65

G.L. Greene et_ «a, Phys. Rev. D ,20, 2139 (1979).

15. F. Bloch and A. Siegert, Phys. Rev. _57, 522 (1940).

16. J.H. Shirley, J. Appl. Phys. 34, 783 (1963), R.F. Code and N.F. Ramsey, Phys.

Rev. A 14, 1945 (1971) and G.L. Greene, Phys. Rev. A18, 1057 (1978).

17. W. Philips, W.E. Cook and D. Kleppner, Phys. Rev. Lett. 35, 1619 (1975).

10 r

18. J.A. Pople, W.G. Schneider and H.J. Bernstein, High Resolution Nuclear

Magnetic Resonance (McGraw Hill, N.Y. 1959).

19. P.F. Winkler, K. Kleppner, T. Myint and F.G. Walther, Phys. Rev. A5, 83 (1973).

20. E.R. Cohen and B.N. Taylor, J. Phys. Chem. Ref. Data 2^ 663 (1973). TABLE 1

Effect Proportion Shift Proportional Error

Bloch-Siegert effect +4.94 x 10" -6 13 x 10 Coil phase errors -1.6 x 10 — 7 —8 Field inhomogeneity <3 x 10~ <4 x 10 Effects of finite -10~ .10 x 10~ velocity distribution

External diamagnetic -4-8 x 10 ' <3 x 10 effects of water

12 r Figure and TabLe Captions

Figure 1 Typical Neutron Resonance

Figure 2 Typical Proton Resonance

Figure 3 Plot of neutron to proton resonance frequencies. The quantity

K(TTI/4I ) (I/I ) is an appropriately scaled oscillating power

which yields a linear fit. (See references in footnote 16 for a

full description). The two orientations correspond to reversals

of the machine axis with respect to the beam velocity.

Table 1 Significant shifts and errors on w /u (cyl, H-0, 22 ). Statistical

error is included in the error assigned to the Bloch-Sitgert effect

and Coil Phase errors.

13 0685004

0685003

0.685002

0685001

0J&85000 - i

0.684999 - \ ^r 0684998 - ^ i 0.684997 - s^ K Onersalion t * Orientation 2 0 0.684996 Mean between 1.2 Lirwar teast square t*s» W nRH/.Oq=. !_.. 1 1 1 I _ 1 1 1 j 0 01 02 Q3 04 05 06 07 08 09 1.0

f,} 3